Abstract

We consider an iterative algorithm for solving a complex matrix equation with conjugate and transpose of two unknowns of the form: +
. With the iterative algorithm, the existence of a solution of this matrix equation can be determined automatically. When this matrix equation is consistent, for any initial matrices , the solutions can be obtained by iterative algorithm within finite iterative steps in the absence of round-off errors. Some lemmas and theorems are stated and proved where the iterative solutions are obtained. A numerical example is given to illustrate the effectiveness of the proposed method and to support the theoretical results of this paper.